Dope failing to finish subsequent lite drink (6,5)

I believe the answer is:

skinny latte

I'm a little stuck... Click here to teach me more about this clue!

'lite drink' is the definition.
'skinny latte' can be an answer for 'drink' (I've seen this before). I'm not sure about the 'lite' bit.

'dope failing to finish subsequent' is the wordplay.
'dope' becomes 'skinny' (I've seen this in another clue).
'failing to finish' means to remove the last letter.
'subsequent' becomes 'latter' (I've seen this in another clue).
'latter' with its final letter taken off is 'latte'.
'skinny'+'latte'='SKINNY LATTE'

Can you help me to learn more?

(Other definitions for skinny latte that I've seen before include "Healthier drink" , "Low-calorie white coffee - sent any kilt (anag)" , "Milky preparation" .)

I've seen this clue in the Sydney Morning Herald.

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